# Introduction to Algebraic Topology (Part-I)

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. Anant R. Shastri
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101144)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101144)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1 : Basic Problem in Topology](https://invisiblenetwork.ai/learn/nptel/111101144/b442ea0bc613) (Video)
2. [Lecture 2 : Concept of homotopy](https://invisiblenetwork.ai/learn/nptel/111101144/adce6eeff5c1) (Video)
3. [Lecture 3 : Bird's eye-view of the course](https://invisiblenetwork.ai/learn/nptel/111101144/97dc3c8ea0eb) (Video)
4. [Lecture 4 : Path Homotopy](https://invisiblenetwork.ai/learn/nptel/111101144/c6ca0cb65cbd) (Video)
5. [Lecture 5 : Composition of paths](https://invisiblenetwork.ai/learn/nptel/111101144/9b28cd9452cc) (Video)
6. [Lecture 6 : Fundamental group π1](https://invisiblenetwork.ai/learn/nptel/111101144/ec807ee1a08d) (Video)
7. [Lecture 7 : Computation of Fund. Group of a circle](https://invisiblenetwork.ai/learn/nptel/111101144/29b5b3a0efb9) (Video)
8. [Lecture 8 : Computation continued](https://invisiblenetwork.ai/learn/nptel/111101144/b694c353aa17) (Video)
9. [Lecture 9 : Computation concluded](https://invisiblenetwork.ai/learn/nptel/111101144/b61e243c7536) (Video)
10. [Lecture 10 : Van-Kampen's Theorem](https://invisiblenetwork.ai/learn/nptel/111101144/a1a6564f5eb0) (Video)
11. [Lecture 11 : Function Spaces](https://invisiblenetwork.ai/learn/nptel/111101144/db4735c99dd2) (Video)
12. [Lecture 12 : Quotient Maps](https://invisiblenetwork.ai/learn/nptel/111101144/9683337df819) (Video)
13. [Lecture 13 : Group Actions](https://invisiblenetwork.ai/learn/nptel/111101144/eb37903d181e) (Video)
14. [Lecture 14 : Examples of Group Actions](https://invisiblenetwork.ai/learn/nptel/111101144/9b4042909e38) (Video)
15. [Lecture 15 : Assorted Results on Quotient Spaces](https://invisiblenetwork.ai/learn/nptel/111101144/967ab6edd75d) (Video)
16. [Lecture 16 : Quotient Constructions Typical to Alg. Top.](https://invisiblenetwork.ai/learn/nptel/111101144/5d94051b0072) (Video)
17. [Lecture 17 : Quotient Constructions continued](https://invisiblenetwork.ai/learn/nptel/111101144/ae27bf687b93) (Video)
18. [Lecture 18 : Relative Homotopy](https://invisiblenetwork.ai/learn/nptel/111101144/3492996b1816) (Video)
19. [Lecture 19 : Construction of a typical SDR](https://invisiblenetwork.ai/learn/nptel/111101144/67b4c65757ff) (Video)
20. [Lecture 20 : Generalized construction of SDRs](https://invisiblenetwork.ai/learn/nptel/111101144/248b90851906) (Video)
21. [Lecture 21 : A theoretical application](https://invisiblenetwork.ai/learn/nptel/111101144/5ad139529e0d) (Video)
22. [Lecture 22 : The Harvest](https://invisiblenetwork.ai/learn/nptel/111101144/48993037e4ac) (Video)
23. [Lecture 23 : NDR pairs](https://invisiblenetwork.ai/learn/nptel/111101144/945db8152372) (Video)
24. [Lecture 24 : General Remarks](https://invisiblenetwork.ai/learn/nptel/111101144/ba5e2d3394b3) (Video)
25. [Lecture 25 : Basics A ne Geometry](https://invisiblenetwork.ai/learn/nptel/111101144/c567b4ab7fc4) (Video)
26. [Lecture 26 : Abstract Simplicial Complex](https://invisiblenetwork.ai/learn/nptel/111101144/c459d60a6550) (Video)
27. [Lecture 27 : Geometric Realization](https://invisiblenetwork.ai/learn/nptel/111101144/5c0428719eeb) (Video)
28. [Lecture 28 : Topology on |K|](https://invisiblenetwork.ai/learn/nptel/111101144/72165f26e39c) (Video)
29. [Lecture 29 : Simplical maps](https://invisiblenetwork.ai/learn/nptel/111101144/0363b4cab4b1) (Video)
30. [Lecture 30 : Polyhedrons](https://invisiblenetwork.ai/learn/nptel/111101144/e9664dedac6d) (Video)
31. [Lecture 31 : Point Set topological Aspects](https://invisiblenetwork.ai/learn/nptel/111101144/d5eebf07ca53) (Video)
32. [Lecture 32 : Barycentric Subdivision](https://invisiblenetwork.ai/learn/nptel/111101144/a3328c13e9be) (Video)
33. [Lecture 33 : Finer Subdivisions](https://invisiblenetwork.ai/learn/nptel/111101144/9f0142a9dc2c) (Video)
34. [Lecture 34 : Simplical Approximation](https://invisiblenetwork.ai/learn/nptel/111101144/949c294ec590) (Video)
35. [Lecture 35 : Sperner Lemma](https://invisiblenetwork.ai/learn/nptel/111101144/8d2e0a3bf20b) (Video)
36. [Lecture 36 : Invariance of domain](https://invisiblenetwork.ai/learn/nptel/111101144/0a3ecd253bae) (Video)
37. [Lecture 37 : Proof of controled homotopy](https://invisiblenetwork.ai/learn/nptel/111101144/02572880460e) (Video)
38. [Lecture 38 : Links and Stars](https://invisiblenetwork.ai/learn/nptel/111101144/8285d6169480) (Video)
39. [Lecture 39 : Homotopical Aspects of Simplicial Complexes](https://invisiblenetwork.ai/learn/nptel/111101144/994c71bfa6f2) (Video)
40. [Lecture 40 : Homotopical Aspects](https://invisiblenetwork.ai/learn/nptel/111101144/c02b4c54dc9d) (Video)
41. [Lecture 41 : Covering Spaces and Fund. Groups](https://invisiblenetwork.ai/learn/nptel/111101144/eb7d31609d1e) (Video)
42. [Lecture 42 : Lifting Properties](https://invisiblenetwork.ai/learn/nptel/111101144/461f0d721d7a) (Video)
43. [Lecture 43 : Homotopy Lifting](https://invisiblenetwork.ai/learn/nptel/111101144/8b03b1b82939) (Video)
44. [Lecture 44 : Relation with the fund. Group](https://invisiblenetwork.ai/learn/nptel/111101144/7ed054365c7d) (Video)
45. [Lecture 45 : Regular covering](https://invisiblenetwork.ai/learn/nptel/111101144/9a4b3cefdea4) (Video)
46. [Lecture 46 : Lifting Problem](https://invisiblenetwork.ai/learn/nptel/111101144/e058d2dbca4a) (Video)
47. [Lecture 47 : Classification of Coverings](https://invisiblenetwork.ai/learn/nptel/111101144/2133e5bccaad) (Video)
48. [Lecture 48 : Classification](https://invisiblenetwork.ai/learn/nptel/111101144/f490467adba0) (Video)
49. [Lecture 49 : Existence of Simply connected coverings](https://invisiblenetwork.ai/learn/nptel/111101144/938ae209402e) (Video)
50. [Lecture 50 : Construction of Simply connected covering](https://invisiblenetwork.ai/learn/nptel/111101144/c9283a7b27f3) (Video)
51. [Lecture 51 : Properties Shared by total space and base](https://invisiblenetwork.ai/learn/nptel/111101144/4b250478c688) (Video)
52. [Lecture 52 : Examples](https://invisiblenetwork.ai/learn/nptel/111101144/e16f76767fd9) (Video)
53. [Lecture 53 : G-coverings](https://invisiblenetwork.ai/learn/nptel/111101144/19bf1ea23104) (Video)
54. [Lecture 54 : Pull-backs](https://invisiblenetwork.ai/learn/nptel/111101144/830f783bd41e) (Video)
55. [Week 11 : Lecture 55](https://invisiblenetwork.ai/learn/nptel/111101144/1a949cc9b30a) (Video)
56. [Lecture 56 : Proof of classification](https://invisiblenetwork.ai/learn/nptel/111101144/ffc56a4bfdf0) (Video)
57. [Lecture 57 : Pushouts and Free products](https://invisiblenetwork.ai/learn/nptel/111101144/0f9b528e8bb9) (Video)
58. [Lecture 58 : Existence of Free Products, pushouts](https://invisiblenetwork.ai/learn/nptel/111101144/f98d3b87354a) (Video)
59. [Lecture 59 : Free Products and free groups](https://invisiblenetwork.ai/learn/nptel/111101144/7e7bbb2ceffb) (Video)
60. [Lecture 60 : Seifert-Van Kampen Theorems](https://invisiblenetwork.ai/learn/nptel/111101144/41f4a739db52) (Video)
61. [Lecture 61 : Applications](https://invisiblenetwork.ai/learn/nptel/111101144/6581c1476022) (Video)
62. [Lecture 62 : Applications continued](https://invisiblenetwork.ai/learn/nptel/111101144/a81243b5e2ed) (Video)
63. [Live Session 05-02-2021](https://invisiblenetwork.ai/learn/nptel/111101144/b442ea0bc613-2) (Video)
64. [Live Session 24-02-2021](https://invisiblenetwork.ai/learn/nptel/111101144/adce6eeff5c1-2) (Video)
65. [Live Session 19-03-2021](https://invisiblenetwork.ai/learn/nptel/111101144/97dc3c8ea0eb-2) (Video)